\begin{tikzpicture}
    \pgfmathsetmacro{\R}{1.5}
    \pgfmathsetmacro{\halfR}{\R/2}

    \tkzDefPoints{0/0/O}
    \tkzDefPoint(270:\R){A}
    \tkzDrawCircle[very thick](O,A)

    \tkzDefRegPolygon[center,sides=10,name=P](O,A)
    \tkzDrawPolygon[thick,red](P1,P...,P10)
    \foreach \P [count=\i from 2] in {B,C,...,J} {
        \coordinate (\P) at (P\i);
    }
    \tkzAutoLabelPoints[center=O, centered, dist= .2](A,B,...,J)
    \tkzLabelPoints[above](O)

    %------ 黄金分割
    \tkzDrawSegment[dashed](O,A)

    % 1
    \tkzDefPointOnLine[pos=0.5](O,A)  \tkzGetPoint{p1}
    \tkzDefLine[perpendicular=through A](O,A)  \tkzGetPoint{p2}
    \tkzInterLC(A,p2)(A,p1)  \tkzGetFirstPoint{P}
    \tkzDrawSegment[dashed](A,P)
    \tkzLabelPoints[below](P)

    % 2
    \tkzDrawSegment[dashed](O,P)
    \tkzInterLC(O,P)(P,A)  \tkzGetFirstPoint{N}
    \tkzDrawArc[towards](P,A)(N)
    % \tkzDrawPoint(N)

    % 3
    \tkzInterLC(O,A)(O,N)  \tkzGetSecondPoint{M}
    \tkzDrawArc[towards](O,N)(M)
    \tkzDrawPoint(M)
    \tkzLabelPoints[right](M)
\end{tikzpicture}

